Modeling of Fluid Introduction and/or Fluid Extraction Elements in Simulation of Coreflood Experiment

ABSTRACT

A coreflood experiment may be modeled by generating a three dimensional computer simulation model of a core plug and modeling within the three dimensional computer simulation model one or both of a fluid introduction element or a fluid extraction element of a core holder used in the coreflood experiment. Once generated, the model may be loaded and used when running a simulation to model a heterogeneous distribution of fluid flow proximate one or more faces of the core plug.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the filing benefit of U.S. Provisional PatentApplication Ser. No. 62/111,158, U.S. Provisional Patent ApplicationSer. No. 62/111,162, and U.S. Provisional Patent Application Ser. No.62/111,166, each of which filed on Feb. 3, 2015, and each of whichincorporated by reference herein in its entirety.

BACKGROUND

Enhanced oil recovery (EOR) is aimed at increasing the recovery factorof oilfields by injecting agents such as chemicals, includingviscoelastic polymers. The design of agent floods for fieldimplementation can impact the success of such operations, both in termsof incremental oil recovery, and in net present value. Reservoirsimulation may be used to assist in the design of such floods, and ithas been found that the accuracy of the reservoir simulation canlikewise impact both the design and the ultimate field implementation.

In addition, reservoir simulation models may be calibrated by usingexperimental data collected during coreflood experiments, during whichcore samples taken from an oilfield are flooded with various fluids tomeasure various flow parameters for the core. Doing so generallyincreases confidence in the experimental data and in simulation results.

SUMMARY

The embodiments disclosed herein provide in one aspect a method ofmodeling a coreflood experiment, which includes generating a threedimensional computer simulation model of a core plug used in a corefloodexperiment and modeling in the three dimensional computer simulationmodel of the core plug one or both of a fluid introduction element or afluid extraction element of a core holder used in the corefloodexperiment.

In some embodiments, the core plug is homogeneous such that the threedimensional computer simulation model has a plurality of grid cellshaving a same property, while in some embodiments, the core plug isheterogeneous such that the three dimensional computer simulation modelhas a plurality of grid cells with varying properties. Some embodimentsalso include running a simulation using the three dimensional computersimulation model in a computer-implemented reservoir simulator to modeldistribution and fingering of fluid flow proximate one or more faces ofthe core plug, and in some embodiments, running the simulation includesmodeling pressure drop across the core plug.

In some embodiments, the computer-implemented reservoir simulatorincludes a general purpose reservoir simulator, generating the threedimensional computer simulation model is performed using a graphicalpre/post-processor for the general purpose reservoir simulator, and themethod further includes displaying simulation results in threedimensions using the graphical pre/post-processor. Also, in someembodiments, the one or both of the fluid introduction element or thefluid extraction element modeled in the three dimensional computersimulation model an end effect in the coreflood experiment, and runningthe simulation includes modeling boundary conditions by representing thefluid introduction element as an injection well and representing thefluid extraction element as a production well. Moreover, in someembodiments, modeling one or both of the fluid introduction element orthe fluid extraction element includes modeling the fluid introductionelement and the fluid extraction element, and in some embodiments,modeling the fluid introduction element and the fluid extraction elementincludes modeling a plurality of ports in each of the fluid introductionelement and the fluid extraction element. In some embodiments, modelingthe fluid introduction element and the fluid extraction element includesmodeling a plurality of channels in each of the fluid introductionelement and the fluid extraction element. In some embodiments, themodeled channels include circular channels and/or radial channels.

Further, in some embodiments, the three dimensional computer simulationmodel has a grid with a resolution that substantially matches that of anuclear magnetic resonance scanner used to determine oil saturation inthe core during the coreflood experiment, and in some embodiments, theone or both of the fluid introduction element or the fluid extractionelement are symmetrical about one or more planes along an axis ofsymmetry of the core plug, and generating the three dimensional computersimulation model and modeling one or both of the fluid introductionelement or the fluid extraction element includes modeling only a segmentof the core plug and the one or both of the fluid introduction elementor the fluid extraction element. In some such embodiments, the fluidintroduction element and the fluid extraction element are eachsymmetrical about a single plane, and generating the three dimensionalcomputer simulation model and modeling one or both of the fluidintroduction element or the fluid extraction element include modelingonly a semi cylinder segment of the core plug and the one or both of thefluid introduction element or the fluid extraction element. In addition,in some such embodiments, the fluid introduction element and the fluidextraction element are each symmetrical about a first and secondorthogonal planes, and generating the three dimensional computersimulation model and modeling one or both of the fluid introductionelement or the fluid extraction element include modeling only a quartercylinder segment of the core plug and the one or both of the fluidintroduction element or the fluid extraction element.

The embodiments disclosed herein may also provide in another aspect amethod of modeling fluid flow through a core plug in a corefloodexperiment, which includes loading a three dimensional computersimulation model of a core plug that additionally models one or both ofa fluid introduction element or a fluid extraction element of a coreholder and running a simulation using the three dimensional computersimulation model in a computer-implemented reservoir simulator to modelheterogeneous distribution of fluid flow proximate one or more faces ofthe core plug.

Other embodiments may include an apparatus including a memory, at leastone processing unit, and program code configured upon execution by theat least one processing unit to perform any of the above-describedoperations. Still other embodiments may include a program productincluding a non-transitory computer readable medium and program codestored on the computer readable medium and configured upon execution byat least one processing unit to perform any of the above-describedoperations.

These and other advantages and features, which characterize theinvention, are set forth in the claims annexed hereto and forming afurther part hereof. However, for a better understanding of theinvention, and of the advantages and objectives attained through itsuse, reference should be made to the Drawings, and to the accompanyingdescriptive matter, in which there is described example embodiments ofthe invention. This summary is merely provided to introduce a selectionof concepts that are further described below in the detaileddescription, and is not intended to identify key or essential featuresof the claimed subject matter, nor is it intended to be used as an aidin limiting the scope of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example hardware and softwareenvironment for a data processing system in accordance withimplementation of various technologies and techniques described herein.

FIGS. 2A-2D illustrate simplified, schematic views of an oilfield havingsubterranean formations containing reservoirs therein in accordance withimplementations of various technologies and techniques described herein.

FIG. 3 illustrates a schematic view, partially in cross section of anoilfield having a plurality of data acquisition tools positioned atvarious locations along the oilfield for collecting data from thesubterranean formations in accordance with implementations of varioustechnologies and techniques described herein.

FIG. 4 illustrates a production system for performing one or moreoilfield operations in accordance with implementations of varioustechnologies and techniques described herein.

FIG. 5 illustrates an example workflow in accordance withimplementations of various technologies and techniques described herein.

FIG. 6 is a functional diagram of an example core holder for a corefloodexperiment.

FIG. 7 is a perspective view of an example core holder platen.

FIG. 8 is an engineering diagram of an example core holder platengeometry.

FIG. 9 illustrates an example three dimensional simulation model of acore plug, and including platens in accordance with implementations ofvarious technologies and techniques described herein.

FIG. 10 illustrates end effects of platens in an example reservoirsimulation performed with the simulation model of FIG. 10.

FIG. 11 is an example graph of a relative permeability model.

FIG. 12 is an example graph of a capillary desaturation function.

FIG. 13 is an example graph of a relative permeability interpretationmodel.

FIG. 14 is an example graph of a comparison of apparent viscosityderived from single-phase corefloods and multi-phase corefloods.

FIG. 15 is an example graph of a comparison of simulation resultsagainst experimental data for an example oil saturation.

FIG. 16 is an example graph of a comparison of simulation resultsagainst experimental data for the pressure drop across an example core.

FIG. 17 illustrates an example sequence of operations for determining anapparent viscosity for an aqueous polymer composition and modeling aflow of the aqueous polymer composition using the determined apparentviscosity in accordance with implementations of various technologies andtechniques described herein.

DETAILED DESCRIPTION

Turning now to the drawings, wherein like numbers denote like partsthroughout the several views, FIG. 1 illustrates an example dataprocessing system 10 in which the various technologies and techniquesdescribed herein may be implemented. System 10 is illustrated asincluding one or more computers 12, e.g., client computers, eachincluding a central processing unit (CPU) 14 including at least onehardware-based processor or processing core 16. CPU 14 is coupled to amemory 18, which may represent the random access memory (RAM) devicescomprising the main storage of a computer 12, as well as anysupplemental levels of memory, e.g., cache memories, non-volatile orbackup memories (e.g., programmable or flash memories), read-onlymemories, etc. In addition, memory 18 may be considered to includememory storage physically located elsewhere in a computer 12, e.g., anycache memory in a microprocessor or processing core, as well as anystorage capacity used as a virtual memory, e.g., as stored on a massstorage device 20 or on another computer coupled to a computer 12.

Each computer 12 also generally receives a number of inputs and outputsfor communicating information externally. For interface with a user oroperator, a computer 12 generally includes a user interface 22incorporating one or more user input/output devices, e.g., a keyboard, apointing device, a display, a printer, etc. Otherwise, user input may bereceived, e.g., over a network interface 24 coupled to a network 26,from one or more external computers, e.g., one or more servers 28 orother computers 12. A computer 12 also may be in communication with oneor more mass storage devices 20, which may be, for example, internalhard disk storage devices, external hard disk storage devices, storagearea network devices, etc.

A computer 12 generally operates under the control of an operatingsystem 30 and executes or otherwise relies upon various computersoftware applications, components, programs, objects, modules, datastructures, etc. For example, one or more petro-technical modules orcomponents 32 executing within an exploration and production (E&P)platform 34 may be used to access, process, generate, modify orotherwise utilize petro-technical data, e.g., as stored locally in adatabase 36 and/or accessible remotely from a collaboration platform 38.Collaboration platform 38 may be implemented using multiple servers 28in some implementations, and it will be appreciated that each server 28may incorporate a CPU, memory, and other hardware components similar toa computer 12. In some embodiments, portions of data processing system10 may be implemented within a cloud computing environment.

In one non-limiting embodiment, for example, the one or morepetro-technical modules 32 may include a graphical pre/post-processor 40such as the PETREL graphical pre/post-processor and a general purposereservoir simulator 42 such as the ECLIPSE reservoir simulator, E&Pplatform 34 may implemented as the PETREL Exploration & Production (E&P)software platform, while collaboration platform 38 may be implemented asthe STUDIO E&P KNOWLEDGE ENVIRONMENT platform, all of which areavailable from Schlumberger Ltd. and its affiliates. It will beappreciated, however, that the techniques discussed herein may beutilized in connection with other platforms and environments, so theinvention is not limited to the particular software platforms andenvironments discussed herein. For example, any of the aforementionedcomponents may be run on a server, on a desktop device, on a mobiledevice, in a cloud computing environment, as a remote desktop or in avirtual machine, etc.

In general, the routines executed to implement the embodiments disclosedherein, whether implemented as part of an operating system or a specificapplication, component, program, object, module or sequence ofinstructions, or even a subset thereof, will be referred to herein as“computer program code,” or simply “program code.” Program codegenerally comprises one or more instructions that are resident atvarious times in various memory and storage devices in a computer, andthat, when read and executed by one or more hardware-based processingunits in a computer (e.g., microprocessors, processing cores, or otherhardware-based circuit logic), cause that computer to perform the stepsembodying desired functionality. Moreover, while embodiments have andhereinafter will be described in the context of fully functioningcomputers and computer systems, those skilled in the art will appreciatethat the various embodiments are capable of being distributed as aprogram product in a variety of forms, and that the invention appliesequally regardless of the particular type of computer readable mediaused to actually carry out the distribution.

Such computer readable media may include computer readable storage mediaand communication media. Computer readable storage media isnon-transitory in nature, and may include volatile and non-volatile, andremovable and non-removable media implemented in any method ortechnology for storage of information, such as computer-readableinstructions, data structures, program modules or other data. Computerreadable storage media may further include RAM, ROM, erasableprogrammable read-only memory (EPROM), electrically erasableprogrammable read-only memory (EEPROM), flash memory or other solidstate memory technology, CD-ROM, DVD, or other optical storage, magneticcassettes, magnetic tape, magnetic disk storage or other magneticstorage devices, or any other medium that can be used to store thedesired information and which can be accessed by computer 10.Communication media may embody computer readable instructions, datastructures or other program modules. By way of example, and notlimitation, communication media may include wired media such as a wirednetwork or direct-wired connection, and wireless media such as acoustic,RF, infrared and other wireless media. Combinations of any of the abovemay also be included within the scope of computer readable media.

Various program code described hereinafter may be identified based uponthe application within which it is implemented in a specific embodimentof the invention. However, it should be appreciated that any particularprogram nomenclature that follows is used merely for convenience, andthus the invention should not be limited to use solely in any specificapplication identified and/or implied by such nomenclature. Furthermore,given the endless number of manners in which computer programs may beorganized into routines, procedures, methods, modules, objects, and thelike, as well as the various manners in which program functionality maybe allocated among various software layers that are resident within atypical computer (e.g., operating systems, libraries, API's,applications, applets, etc.), it should be appreciated that theinvention is not limited to the specific organization and allocation ofprogram functionality described herein.

Furthermore, it will be appreciated by those of ordinary skill in theart having the benefit of the instant disclosure that the variousoperations described herein that may be performed by any program code,or performed in any routines, workflows, or the like, may be combined,split, reordered, omitted, and/or supplemented with other techniquesknown in the art, and therefore, the invention is not limited to theparticular sequences of operations described herein.

Those skilled in the art will recognize that the example environmentillustrated in FIG. 1 is not intended to limit the invention. Indeed,those skilled in the art will recognize that other alternative hardwareand/or software environments may be used without departing from thescope of the invention.

Oilfield Operations

FIGS. 2A-2D illustrate simplified, schematic views of an oilfield 100having subterranean formation 102 containing reservoir 104 therein inaccordance with implementations of various technologies and techniquesdescribed herein. FIG. 2A illustrates a survey operation being performedby a survey tool, such as seismic truck 106.1, to measure properties ofthe subterranean formation. The survey operation is a seismic surveyoperation for producing sound vibrations. In FIG. 2A, one such soundvibration, sound vibration 112 generated by source 110, reflects offhorizons 114 in earth formation 116. A set of sound vibrations isreceived by sensors, such as geophone-receivers 118, situated on theearth's surface. The data received 120 is provided as input data to acomputer 122.1 of a seismic truck 106.1, and responsive to the inputdata, computer 122.1 generates seismic data output 124. This seismicdata output may be stored, transmitted or further processed as desired,for example, by data reduction.

FIG. 2B illustrates a drilling operation being performed by drillingtools 106.2 suspended by rig 128 and advanced into subterraneanformations 102 to form wellbore 136. Mud pit 130 is used to drawdrilling mud into the drilling tools via flow line 132 for circulatingdrilling mud down through the drilling tools, then up wellbore 136 andback to the surface. The drilling mud may be filtered and returned tothe mud pit. A circulating system may be used for storing, controlling,or filtering the flowing drilling muds. The drilling tools are advancedinto subterranean formations 102 to reach reservoir 104. Each well maytarget one or more reservoirs. The drilling tools are adapted formeasuring downhole properties using logging while drilling tools. Thelogging while drilling tools may also be adapted for taking core sample133 as shown.

Computer facilities may be positioned at various locations about theoilfield 100 (e.g., the surface unit 134) and/or at remote locations.Surface unit 134 may be used to communicate with the drilling toolsand/or offsite operations, as well as with other surface or downholesensors. Surface unit 134 is capable of communicating with the drillingtools to send commands to the drilling tools, and to receive datatherefrom. Surface unit 134 may also collect data generated during thedrilling operation and produces data output 135, which may then bestored or transmitted.

Sensors (S), such as gauges, may be positioned about oilfield 100 tocollect data relating to various oilfield operations as describedpreviously. As shown, sensor (S) is positioned in one or more locationsin the drilling tools and/or at rig 128 to measure drilling parameters,such as weight on bit, torque on bit, pressures, temperatures, flowrates, compositions, rotary speed, and/or other parameters of the fieldoperation. Sensors (S) may also be positioned in one or more locationsin the circulating system.

Drilling tools 106.2 may include a bottom hole assembly (BHA) (notshown), generally referenced, near the drill bit (e.g., within severaldrill collar lengths from the drill bit). The bottom hole assemblyincludes capabilities for measuring, processing, and storinginformation, as well as communicating with surface unit 134. The bottomhole assembly further includes drill collars for performing variousother measurement functions.

The bottom hole assembly may include a communication subassembly thatcommunicates with surface unit 134. The communication subassembly isadapted to send signals to and receive signals from the surface using acommunications channel such as mud pulse telemetry, electro-magnetictelemetry, or wired drill pipe communications. The communicationsubassembly may include, for example, a transmitter that generates asignal, such as an acoustic or electromagnetic signal, which isrepresentative of the measured drilling parameters. It will beappreciated by one of skill in the art that a variety of telemetrysystems may be employed, such as wired drill pipe, electromagnetic orother known telemetry systems.

Generally, the wellbore is drilled according to a drilling plan that isestablished prior to drilling. The drilling plan sets forth equipment,pressures, trajectories and/or other parameters that define the drillingprocess for the wellsite. The drilling operation may then be performedaccording to the drilling plan. However, as information is gathered, thedrilling operation may need to deviate from the drilling plan.Additionally, as drilling or other operations are performed, thesubsurface conditions may change. The earth model may also needadjustment as new information is collected

The data gathered by sensors (S) may be collected by surface unit 134and/or other data collection sources for analysis or other processing.The data collected by sensors (S) may be used alone or in combinationwith other data. The data may be collected in one or more databasesand/or transmitted on or offsite. The data may be historical data, realtime data, or combinations thereof. The real time data may be used inreal time, or stored for later use. The data may also be combined withhistorical data or other inputs for further analysis. The data may bestored in separate databases, or combined into a single database.

Surface unit 134 may include transceiver 137 to allow communicationsbetween surface unit 134 and various portions of the oilfield 100 orother locations. Surface unit 134 may also be provided with orfunctionally connected to one or more controllers (not shown) foractuating mechanisms at oilfield 100. Surface unit 134 may then sendcommand signals to oilfield 100 in response to data received. Surfaceunit 134 may receive commands via transceiver 137 or may itself executecommands to the controller. A processor may be provided to analyze thedata (locally or remotely), make the decisions and/or actuate thecontroller. In this manner, oilfield 100 may be selectively adjustedbased on the data collected. This technique may be used to optimizeportions of the field operation, such as controlling drilling, weight onbit, pump rates, or other parameters. These adjustments may be madeautomatically based on computer protocol, and/or manually by anoperator. In some cases, well plans may be adjusted to select optimumoperating conditions, or to avoid problems.

FIG. 2C illustrates a wireline operation being performed by wirelinetool 106.3 suspended by rig 128 and into wellbore 136 of FIG. 2B.Wireline tool 106.3 is adapted for deployment into wellbore 136 forgenerating well logs, performing downhole tests and/or collectingsamples. Wireline tool 106.3 may be used to provide another method andapparatus for performing a seismic survey operation. Wireline tool 106.3may, for example, have an explosive, radioactive, electrical, oracoustic energy source 144 that sends and/or receives electrical signalsto surrounding subterranean formations 102 and fluids therein.

Wireline tool 106.3 may be operatively connected to, for example,geophones 118 and a computer 122.1 of a seismic truck 106.1 of FIG. 2A.Wireline tool 106.3 may also provide data to surface unit 134. Surfaceunit 134 may collect data generated during the wireline operation andmay produce data output 135 that may be stored or transmitted. Wirelinetool 106.3 may be positioned at various depths in the wellbore 136 toprovide a survey or other information relating to the subterraneanformation 102.

Sensors (S), such as gauges, may be positioned about oilfield 100 tocollect data relating to various field operations as describedpreviously. As shown, sensor S is positioned in wireline tool 106.3 tomeasure downhole parameters which relate to, for example porosity,permeability, fluid composition and/or other parameters of the fieldoperation.

FIG. 2D illustrates a production operation being performed by productiontool 106.4 deployed from a production unit or Christmas tree 129 andinto completed wellbore 136 for drawing fluid from the downholereservoirs into surface facilities 142. The fluid flows from reservoir104 through perforations in the casing (not shown) and into productiontool 106.4 in wellbore 136 and to surface facilities 142 via gatheringnetwork 146.

Sensors (S), such as gauges, may be positioned about oilfield 100 tocollect data relating to various field operations as describedpreviously. As shown, the sensor (S) may be positioned in productiontool 106.4 or associated equipment, such as christmas tree 129,gathering network 146, surface facility 142, and/or the productionfacility, to measure fluid parameters, such as fluid composition, flowrates, pressures, temperatures, and/or other parameters of theproduction operation.

Production may also include injection wells for added recovery. One ormore gathering facilities may be operatively connected to one or more ofthe wellsites for selectively collecting downhole fluids from thewellsite(s).

While FIGS. 2B-2D illustrate tools used to measure properties of anoilfield, it will be appreciated that the tools may be used inconnection with non-oilfield operations, such as gas fields, mines,aquifers, storage, or other subterranean facilities. Also, while certaindata acquisition tools are depicted, it will be appreciated that variousmeasurement tools capable of sensing parameters, such as seismic two-waytravel time, density, resistivity, production rate, etc., of thesubterranean formation and/or its geological formations may be used.Various sensors (S) may be located at various positions along thewellbore and/or the monitoring tools to collect and/or monitor thedesired data. Other sources of data may also be provided from offsitelocations.

The field configurations of FIGS. 2A-2D are intended to provide a briefdescription of an example of a field usable with oilfield applicationframeworks. Part, or all, of oilfield 100 may be on land, water, and/orsea. Also, while a single field measured at a single location isdepicted, oilfield applications may be utilized with any combination ofone or more oilfields, one or more processing facilities and one or morewellsites.

FIG. 3 illustrates a schematic view, partially in cross section ofoilfield 200 having data acquisition tools 202.1, 202.2, 202.3 and 202.4positioned at various locations along oilfield 200 for collecting dataof subterranean formation 204 in accordance with implementations ofvarious technologies and techniques described herein. Data acquisitiontools 202.1-202.4 may be the same as data acquisition tools 106.1-106.4of FIGS. 2A-2D, respectively, or others not depicted. As shown, dataacquisition tools 202.1-202.4 generate data plots or measurements208.1-208.4, respectively. These data plots are depicted along oilfield200 to demonstrate the data generated by the various operations.

Data plots 208.1-208.3 are examples of static data plots that may begenerated by data acquisition tools 202.1-202.3, respectively, however,it should be understood that data plots 208.1-208.3 may also be dataplots that are updated in real time. These measurements may be analyzedto better define the properties of the formation(s) and/or determine theaccuracy of the measurements and/or for checking for errors. The plotsof each of the respective measurements may be aligned and scaled forcomparison and verification of the properties.

Static data plot 208.1 is a seismic two-way response over a period oftime. Static plot 208.2 is core sample data measured from a core sampleof the formation 204. The core sample may be used to provide data, suchas a graph of the density, porosity, permeability, or some otherphysical property of the core sample over the length of the core. Testsfor density and viscosity may be performed on the fluids in the core atvarying pressures and temperatures. Static data plot 208.3 is a loggingtrace that generally provides a resistivity or other measurement of theformation at various depths.

A production decline curve or graph 208.4 is a dynamic data plot of thefluid flow rate over time. The production decline curve generallyprovides the production rate as a function of time. As the fluid flowsthrough the wellbore, measurements are taken of fluid properties, suchas flow rates, pressures, composition, etc.

Other data may also be collected, such as historical data, user inputs,economic information, and/or other measurement data and other parametersof interest. As described below, the static and dynamic measurements maybe analyzed and used to generate models of the subterranean formation todetermine characteristics thereof. Similar measurements may also be usedto measure changes in formation aspects over time.

The subterranean structure 204 has a plurality of geological formations206.1-206.4. As shown, this structure has several formations or layers,including a shale layer 206.1, a carbonate layer 206.2, a shale layer206.3 and a sand layer 206.4. A fault 207 extends through the shalelayer 206.1 and the carbonate layer 206.2. The static data acquisitiontools are adapted to take measurements and detect characteristics of theformations.

While a specific subterranean formation with specific geologicalstructures is depicted, it will be appreciated that oilfield 200 maycontain a variety of geological structures and/or formations, sometimeshaving extreme complexity. In some locations, generally below the waterline, fluid may occupy pore spaces of the formations. Each of themeasurement devices may be used to measure properties of the formationsand/or its geological features. While each acquisition tool is shown asbeing in specific locations in oilfield 200, it will be appreciated thatone or more types of measurement may be taken at one or more locationsacross one or more fields or other locations for comparison and/oranalysis.

The data collected from various sources, such as the data acquisitiontools of FIG. 3, may then be processed and/or evaluated. Generally,seismic data displayed in static data plot 208.1 from data acquisitiontool 202.1 is used by a geophysicist to determine characteristics of thesubterranean formations and features. The core data shown in static plot208.2 and/or log data from well log 208.3 are generally used by ageologist to determine various characteristics of the subterraneanformation. The production data from graph 208.4 is generally used by thereservoir engineer to determine fluid flow reservoir characteristics.The data analyzed by the geologist, geophysicist and the reservoirengineer may be analyzed using modeling techniques.

FIG. 4 illustrates an oilfield 300 for performing production operationsin accordance with implementations of various technologies andtechniques described herein. As shown, the oilfield has a plurality ofwellsites 302 operatively connected to central processing facility 354.The oilfield configuration of FIG. 4 is not intended to limit the scopeof the oilfield application system. Part or all of the oilfield may beon land and/or sea. Also, while a single oilfield with a singleprocessing facility and a plurality of wellsites is depicted, anycombination of one or more oilfields, one or more processing facilitiesand one or more wellsites may be present.

Each wellsite 302 has equipment that forms wellbore 336 into the earth.The wellbores extend through subterranean formations 306 includingreservoirs 304. These reservoirs 304 contain fluids, such ashydrocarbons. The wellsites draw fluid from the reservoirs and pass themto the processing facilities via surface networks 344. The surfacenetworks 344 have tubing and control mechanisms for controlling the flowof fluids from the wellsite to processing facility 354.

EOR Chemical Coreflood Simulation Study Workflow

Chemical EOR processes, such as surfactant or polymer flooding (amongothers), are used in the oil and gas industry to improve the recovery ofhydrocarbons. In order to design these processes, laboratory experimentssuch as coreflood experiments, may be used. Coreflood experiments,however, generally look at very small scales, e.g., using cores (alsoreferred to herein as core plugs) that are at most several centimetersin diameter and length, and experiments on cores are generallytime-consuming. Pilot studies may also be used to design theseprocesses; however implementing such pilot studies can be very expensiveand collecting results can take a substantial amount of time. Reservoirsimulation offers the potential for being cheaper and faster, therebypotentially facilitating the EOR design process.

In this regard, EOR chemical flooding, or coreflooding, generally refersto the injection of a chemical composition including one or morechemical agents suitable for use in connection with enhanced oilrecovery. Such compositions may include, in some embodiments, one ofmore chemical structures each with one or more molecular weights thattogether with zero, one or more subsidiary components such as salts, pHadjusters or surfactants form an aqueous solution. In the embodimentsdiscussed below, for example, the focus is on polymer flooding usingaqueous polymer solutions incorporating one or more polymers along withany of the aforementioned subsidiary components. Any references hereinto polymers therefore may be considered to refer to various aqueouspolymer compositions. It will appreciated, however, that other EORchemical floods, using other EOR chemicals (including, for example,formation water, low salinity water, surfactant, alkali, polymer gel,foam, nanoparticles, other chemical additives, some combination of twoor more of the aforementioned EOR agents, etc.) may be used in otherembodiments, so the invention is not limited specifically to polymerflooding.

Embodiments consistent with the invention may be used to model in areservoir simulator the results of an EOR chemical coreflood experimentand thereby generate a coreflood simulation model. As such, a generalpurpose reservoir simulator conventionally used for modeling anoilfield, e.g., the ECLIPSE reservoir simulator available fromSchlumberger Ltd. and its affiliates, among others, may be used to modelan EOR chemical coreflood experiment. In this regard, the term “generalpurpose reservoir simulator” is used to refer to a reservoir simulatorthat is used for modeling an oilfield, as opposed to a special purposesimulator built specifically to model a core or a coreflood experiment.

Moreover, in the embodiments discussed hereinafter, the term “core” or“core plug” may be used to refer to rock core samples extracted from awellbore, as well as other bodies upon which a coreflood experiment maybe performed, including, for example, reconstituted cores, sandpacks,bead packs, etc. Further, while the embodiments discussed hereinaftermay refer to water floods, it will be appreciated that the term “water”may be used to refer to other types of aqueous solutions includingdifferent brine formulations.

An example workflow is disclosed herein, in particular, to demonstratethe feasibility of an EOR chemical coreflood simulation study using theECLIPSE reservoir simulator. The invention, however, may be utilized inconnection with other reservoir simulators, so the invention is notlimited to use solely with the ECLIPSE reservoir simulator as usedherein. It will be appreciated that the workflow may be implementedsolely within a computer environment and with the use of one or moreprocessors in some embodiments, whereas in other embodiments, some actsor operations in the work flow may be performed by a user outside of thecomputer environment, with other acts or operations performed with theuse of one or more processors.

FIG. 5 illustrates an example workflow 400, which may be performed toprocess the results of an EOR chemical coreflood experiment, and inparticular, a polymer coreflood experiment, and thereby conduct apolymer coreflood simulation study for enhanced oil recovery throughreservoir simulation for a viscoelastic polymer. As will be appreciated,viscoelastic polymers may be injected into a reservoir along with wateror another fluid to form an aqueous polymer composition and therebyincrease the overall viscosity of the injected composition, among otherreasons, and one goal of an EOR chemical coreflood simulation study isto attempt to predict an increase in production as a result of a fieldimplementation of an EOR operation.

Workflow 400 may begin as illustrated in block 402 by performinganalysis of the lab experiments. For example, the experimental apparatusand experimental protocol used for the experiments may be analyzed, asmay how the data was measured and the precision to which the data wasmeasured in the experiments. Doing so enables suitable reservoirsimulator parameters to be determined prior to building a simulationmodel.

In some embodiments, for example, an experiment may be performed on acore sample of substantially homogeneous material within a core holderthat includes fluid introduction and extraction elements referred to asplatens that allow fluids to circulate through the core, and that aredesigned to distribute the entry and exit of fluids in the core across alarge area of the faces of the core.

In one non-limiting example experiment, the core may be filled with oil,e.g., at a rate of about 10 cm³/min during 20 PV, until the core issubstantially saturated with oil (e.g., about 96%). An initial water(brine) flood may then be performed at a constant rate, e.g., at about0.2 cm³/min during 20 PV, during which a relatively large initialresidual oil saturation (e.g., about 64%) may be reached. Then, anotherwater (brine) flood may be performed at incremental or stepwiseincreasing flow rates, e.g., ranging from about 0.01 cm³/min to about100 cm³/min. Subsequently, a polymer flood (e.g., with an aqueouspolymer composition comprising an anionic polysaccharide such as Xanthanand a partially hydrolyzed polyacrylamide (HPAM) synthetic polyanion),may also be performed at incremental or stepwise increasing flow rates,e.g., ranging from about 0.01 cm³/min to about 100 cm³/min. Thereafter,the core may be flushed with water or brine at about 0.01 cm³/min during30 PV to flush out any polymer remaining within the core and enable theexperiment to be repeated for other aqueous polymer compositions. Duringeach flood, measurements may be made of both pressure (e.g., at theentrance and outlet to derive a pressure drop across the core) and oilsaturation (e.g., using nuclear magnetic resonance (NMR) measurements inthe middle-third of the core to minimize end-effects introduced by theplatens).

Next, in block 404, detailed modeling may be performed to create athree-dimensional (3D) simulation model in the reservoir simulatorcapturing the design of the experiment. In particular, a 3D simulationmodel of the core sample may be created, mirroring the geometry of thecore sample and partitioned into a three dimensional grid of cells. Insome embodiments, the core sample may be treated as a homogeneousmaterial, such that all of the grid cells associated with the coresample are assigned the same property values such as porosity andpermeability. In addition, in some embodiments, and as will be describedin greater detail below, additional aspects of the experimentalapparatus, e.g., the core holder platens, may also be incorporated intothe simulation model to more effectively model end effects. In otherembodiments, however, a core sample may be treated as a heterogeneousmaterial, with some or all of the grid cells associated with the coresample having varying property values.

Next, in block 406, the data may be reviewed, e.g., by performing dataquality analysis and quality control to identify uncertainty on thedata, and potential errors in the data due to calibration of measurementdevices or other sources of inaccuracy.

Next, in block 408, three simulation studies 410, 412 and 414 may beperformed in consecutive stages to validate the data. First, in study410, the water (brine) flood at constant flow rate is analyzed. Study410, in particular, may ensure that data such as the fluid model (oil,water), the rock properties (porosity, permeability, relativepermeability) and the simulation model itself are defined accurately. Asnoted above, in the example experiment, water or brine is injected intoa core that is full of oil, and the constant flow rate flood reduces theoil saturation to a residual oil saturation as defined by relativepermeability curves. Validation may occur by comparing the result of thewater flood against calculated results based on Darcy's law.

Second, in study 412, the water (brine) flood an incremental flow ratesis analyzed. A capillary desaturation model may be used to represent thefurther decrease of oil saturation beyond the residual oil saturation.This capillary desaturation model may include an interpolation betweenthe relative permeability curves defined in the previous study, andhypothetical relative permeability curves corresponding to a state wherethe rock is fully stripped from the oil (i.e., where residual oilsaturation is decreased to zero). During this study, the simulatedinterpolated relative permeability may be compared to the relativepermeability derived from the experimental data using Darcy's law. Thisstep may be used, for example, to validate the capillary desaturationmodel and the relative permeability curves that are used for simulation.It will be appreciated that studies 410-412 effectively establish awater base case, representing the amount of oil desaturation obtainablethrough water flooding alone, and against which the performance of theEOR chemical flood (e.g., in terms of additional observed reduction inresidual oil saturation as a result of the EOR chemical flood) may becompared. In this regard, a water base case may be considered in someembodiments to be a base case established for the simulation model inwhich water, substantially free of other chemical additives, is injectedinto the core.

Third, in study 414, the polymer flood at incremental flow rates isanalyzed. This study may use the capillary desaturation model and thevalidated relative permeability curves from the previous study. Polymerproperties may be characterized and input to the simulation. Polymerproperties may include, for example, solution viscosity as a function ofthe solution concentration, polymer solution shear rheology (relatingthe solution's shear viscosity with the water velocity), adsorptionproperties (e.g., tables of adsorbed polymer as a function of polymerconcentration surrounding the rock, rock density, maximum adsorptionconcentration, and resulting maximum residual resistance factor, andwhether the polymer can desorb from the rock), an inaccessible porevolume fraction (e.g., to estimate the proportion of pore volume thatwill not be penetrated by the polymer solution), etc. Additionalproperties, e.g., apparent viscosity (viscosity under shear stress whenthe polymer is injected in the rock) may not be known during amulti-phase flood and may be calculated.

It will be appreciated that polymer properties may more broadly beconsidered to be types of EOR chemical properties. Further, for EORchemical floods using compositions other than aqueous polymer solutions,other types of properties relevant to the particular EOR chemicalsutilized in such floods (e.g., adsorption rates, decay rates, chemicalreaction rates, mobility reduction effects, interfacial tension,capillary pressure, temperature effects, shear rates, relativepermeability hysteresis effects, etc.) may also be studied in acorresponding manner. As such, the invention is not limited to theparticular study and analyzed properties disclosed herein in connectionwith a polymer coreflood with an aqueous polymer solution.

Upon completion of study 414, the workflow may return to block 406 toperform additional data review, e.g., to perform sensitivity analysis toinvestigate the impact of various uncertain simulation and/or physicalparameters on the match between the simulation and experimental data.Thus, blocks 406 and 408 may be repeated multiple iterations in someinstances (e.g., using history matching) to iteratively calibrate thereservoir simulation model and better match the experimental results. Inaddition, as illustrated by block 416, each stage or study 410-414 mayalso include iterative data review and corrections performed as desiredto calibrate the reservoir simulation model.

In some embodiments of the invention, therefore, once a simulation modelis designed to reproduce the experimental setup, an initial water orbrine flood at a constant injection rate may be simulated and comparedagainst experimental data to validate the simulation model. Then, thewater or brine floods at incremental injection rates may be simulatedand matched to the experimental data to validate the relativepermeability curves and the modeling of the observed reduction inresidual oil saturation. Thereafter, the EOR chemical floods may besimulated and matched to the experimental data to establish appropriateinput parameters for the EOR chemical properties and to validate themodels embedded in the reservoir simulator. Sensitivity analysis maythereafter be performed to investigate the impact of a number ofuncertain simulation and physical parameters on the match between thesimulation and the experimental data, and the simulation model may berevised accordingly.

In addition, it will be appreciated that validation of a model may beperformed in various manners, as will be appreciated by those ofordinary skill in the art having the benefit of the instant disclosure.For example, in some embodiments, the reservoir simulator may produceoutput summary data including numerical values of pressure, flow rates,fluid saturations, etc. for each simulated time step, and this outputdata may be compared directly with the observed experimental results, orused to calculate derived quantities for comparison with theexperimental results.

As also illustrated in block 418, once the simulation model is generatedand validated in the manner described above, the simulation model maythereafter be used in connection with other coreflood and/or reservoirsimulations. In addition, performing simulations with the simulationmodel either in connection with generating and validating the model orusing the model for other simulations may result in the generation ormodeling of various properties, including, for example, one or more offluid flow, fluid distribution in a core, pressure drop across a core,or other properties that will be appreciated by those of ordinary skillin the art.

It will be appreciated that the manner in which workflow 400 may beimplemented may vary in different embodiments. In some embodiments, forexample, a graphical pre/post-processor, e.g., the PETREL graphicalpre/post-processor, in communication with a general purpose reservoirsimulator such as the ECLIPSE reservoir simulator, may be used inconnection with the performance of a number of steps in the workflow,including, for example, generating the model, performing theaforementioned simulation studies on the simulation model, validatingthe simulation model, inputting data into the reservoir simulator,examining experimental data to check validity, visualizing simulationresults (including visualizing results in one, two, three or moredimensions), and examining simulation results for comparison with theexperimental data, among others. In addition, in some embodiments, someor all of the workflow may be implemented using a plug-in or script,e.g., to perform one or more of building a model, performingcalculations to define input parameters, interpreting simulationresults, comparing results with observed or experimental data,performing multiple realizations for sensitivity analysis, historymatching, etc.

Thus, in some embodiments, a coreflood simulation model may be generatedby generating a three-dimensional computer simulation model of a coreplug used in a coreflood experiment in a computer-implemented generalpurpose reservoir simulator, performing one or more simulation studieson the simulation model to establish a water base case for thesimulation model, and after performing the one or more simulationstudies on the simulation model, performing an additional simulationstudy on the simulation model to establish one or more EOR chemicalproperties and to further validate the simulation model by simulating anEOR chemical flood at a plurality of incremental flow rates.

Further, in some embodiments, a coreflood may be simulated by loading athree dimensional computer simulation model of a core plug used in acoreflood experiment and validated by performing one or more simulationstudies on the simulation model to establish a water base case for thesimulation model and by performing an additional simulation study on thesimulation model to establish one or more EOR chemical properties fromsimulation of an EOR chemical flood at a plurality of incremental flowrate, and running a simulation using the three-dimensional computersimulation model of the core plug in the computer-implemented generalpurpose reservoir simulator.

Modeling of Fluid Introduction Apparatus in Reservoir Simulation

As noted above, coreflood experiments may be performed by placing a coreplug in a core holder. The core holder generally has fluid introductionand extraction elements referred to as platens that allow the fluids tocirculate through the core, and that are designed to distribute theentry and exit of the fluids in the core across a relatively large areaof the faces of the core.

It has been found that when the core length is small, it is desirable toidentify the end effects that could be due to the geometry of theplatens that lead to a homogenization of the flow further away in thecore, or due to capillary effects. To do that, and as noted above, thegeometry of the platens may be included in a three dimensionalsimulation model of the core plug to be more representative of thelaboratory experiment.

FIG. 6, for example, illustrates an example core holder 420 for acoreflood experiment, where a core plug 422 is retained within apressure confinement sleeve 424 with fluid introduction and extractionelements or platens 426, 428 disposed on the opposing faces of the coreplug 422, with the introduction and extraction of fluids represented inthe bottom and top of the figure.

Various platen designs may be used to distribute fluid across each faceof the core plug 422. FIG. 7 illustrates one such platen design forfluid introduction element or platen 426, which may be used in someembodiments of the invention. In this design, a surface 440 that facesthe core plug includes four symmetrically-disposed inlet ports 444 influid communication with a pair of concentric circular recessed channels446, 448 through a pair of orthogonal radial recessed channels 450, 452.In some embodiments, an identical platen design to that illustrated inFIG. 7 may be used for a fluid extraction element or platen to extractfluid through four symmetrically-disposed outlet ports. It will beappreciated that an innumerable number of variations, includingdifferent numbers and/or layouts of ports, and different numbers,layouts and/or orientations of channels, may be used for the fluidintroduction and fluid extraction elements in other embodiments, so theinvention is not limited to the particular design illustrated herein.

In some embodiments of the invention, it may be desirable to model theplatens in three dimensions directly as part of a simulation grid. Thedimensions of all of the flow conducting channels that have beendesigned to distribute the flow across the face of the core may bedetermined in order to incorporate the design within the simulationgrid, and in some embodiments, detailed engineering diagrams, e.g., asshown at 460 in FIG. 8, may be used to integrate the platen design, andin particular, the channels defined by the platen, into the simulationgrid. In some embodiments, software such as available in the PETRELsoftware platform may be used in this process.

The resulting framework may then be used to construct a full threedimensional model that captures the overall design of the core plug andthe platens, e.g., as illustrated at 470 in FIG. 9, where the top of thefigure represents the outlet platen, with the inlet platen also includedin the model but not shown by virtue of the orientation of the figure.An end surface 472 represents the mating surface between the outletplaten and the end of the core, with channels modeled as illustrated at474 and outlet ports modeled as illustrated at 476. The impact ofmodeling such an apparatus is observed by visualizing the distributionof fluids either when running the simulation or when the simulation hascompleted. FIG. 10, for example, is a cross-sectional view of the model,and it can be seen by the difference in shading proximate the platensthe heterogeneous distribution of fluid flow proximate the faces of thecore plug, and thus the end effects experienced during a corefloodexperiment. As such, model 470 may be used in some embodiments to modelthe distribution and fingering of fluid flow proximate one or more facesof a core plug.

Returning to FIG. 9, it may be desirable in some embodiments to set theplaten channels 474 in the model to have a porosity of 1 (assuming thechannels do not include a porous material) and a high permeability toaccurately represent the flow characteristics of the platen channelsrelative to the core plug. Boundary conditions for the resulting modelmay be modeled by injection wells (for the inlet platen) and productionwells (for the outlet platen) perforated at injection points in theplaten that were used in the experiment to represent the pipingconnected to the core holder system (e.g., as illustrated at 476 for theoutlet platen). Injection wells may be assigned to the same group andcontrolled by a group injection rate since the flow rate controlled bythe pump is that of the main pipe that splits into the various injectionpoints. This group injection rate may therefore be set as the pump rate.The production wells may be controlled by a bottom hole pressure limitset to 1 atm, since the outlet piping connects to atmospheric pressure.

In some embodiments, if the injection and/or production systems aresymmetric about one or more planes along an axis of symmetry of the coreplug, and the core plug may be treated as homogeneous, an evendistribution of flow in each inlet/outlet port may be assumed, and themodel may be simplified to a segment representing only a portion of thefull model, e.g., as shown by quarter cylinder segment 480 in FIG. 10(segmented along two orthogonal planes P1 and P2 about the core's axisof symmetry), which may result in faster simulations (due to the reducednumber of cells) with comparable accuracy. In other embodiments,symmetry may exist in fewer or greater numbers of planes. In one otherembodiment, for example, the injection and production systems may besymmetric about a single plane, such that a semi cylinder segment may beused.

The size or resolution of the simulation grid used for a model may varyin different embodiments. For example, in some embodiments, it may bedesirable to use a resolution that substantially matches that of anuclear magnetic resonance scanner used to determine oil saturation inthe core during a coreflood experiment. Other resolutions, however, maybe used in other embodiments.

It will be appreciated that by modeling the fluid introduction andextraction elements or platens, end effects may be simulated to providea more accurate simulation. In some embodiments, this may allow shorterand/or narrower core plugs to be used in experiments. Further, in someembodiments, the herein-described techniques may be used in the designof fluid introduction and extraction elements or platens, e.g., toconfirm whether a particular design provides a desired fluid flow for aparticular application.

Thus, in some embodiments, a coreflood experiment may be modeled bygenerating a three dimensional computer simulation model of a core plugused in a coreflood experiment, and modeling in the three dimensionalcomputer simulation model of the core plug one or both of a fluidintroduction element or a fluid extraction element of a core holder usedin the coreflood experiment. Further, in some embodiments, fluid flowthrough a core plug in a coreflood experiment may be modeled by loadinga three dimensional computer simulation model of a core plug thatadditionally models one or both of a fluid introduction element or afluid extraction element of a core holder, and running a simulationusing the three dimensional computer simulation model in acomputer-implemented reservoir simulator to model heterogeneousdistribution of fluid flow proximate one or more faces of the core plug.

Multi-Phase Polymer Shear Viscosity Calculation

In some embodiments, simulation accuracy, particularly for thesimulation of aqueous polymer composition injection, may be furtherimproved by estimating one or more properties of the aqueous polymercomposition (e.g., apparent viscosity, i.e., viscosity under shearstress when injected in the core) during a multi-phase coreflood.

It has been found, for example, that the apparent viscosity of anaqueous polymer composition may be straightforwardly calculated during asingle-phase flood using Darcy's law. However, for a multi-phase flood,Darcy's law includes an additional term in the equation for each phase:the relative permeability of that phase. For example the water flowdepends on the water relative permeability. When the residual oilsaturation is decreased beyond its initial value (capillarydesaturation), there is a change of the water relative permeability thatmay be difficult to characterize through measurements, therebycomplicating the calculation of apparent viscosity.

In some embodiments of the invention, apparent viscosity of an aqueouspolymer composition, e.g., including one or more viscoelastic polymers,during a multi-phase coreflood experiment may be calculated using aworkflow that in part utilizes data from the aforementioned water orbrine floods performed with stepwise incremented flow rates. These typesof floods may be used to verify that the relative permeabilityinterpolation model associated with capillary desaturation areappropriate. Then, these relative permeability curves may be used tocalculate the relative permeability of an aqueous polymer compositionduring the multi-phase flood, based on the state of oil saturation inthe core. The relative permeability points may then be used to calculatethe apparent viscosity of the aqueous polymer composition using Darcy'slaw, and the resulting calculation may then be validated by matching thesimulation model to the coreflood experimental results.

A capillary desaturation function may be used to account for thereduction in residual oil saturation occurring during a multi-phaseflood of aqueous polymer composition into oil with increasing injectionflow rate. The model may interpolate relative permeability curvesbetween relative permeability curves associated with the residual oilsaturation of the initial brine flood, and curves assuming that theresidual oil saturation is taken down to 0, e.g., as shown in FIG. 11. Awater or brine flood experiment at varying flow rates may be performedand matched in order to validate the relative permeability curvesinterpolation. The water relative permeability obtained in thesimulation may also be compared with the curve derived from thelaboratory measurements.

To calculate the relative permeability to water, Darcy's law may beapplied:

$\begin{matrix}{k_{rw} = \frac{Q\; \mu \; L}{{kA}\; \Delta \; P}} & \left( {{Eq}.\mspace{14mu} 1} \right)\end{matrix}$

where k_(rw) is the relative permeability to water, Q is the injectionflow rate in m³/s, μ is the viscosity in Pa·s, L is the length of thecore, k is the absolute permeability of the rock, A is the crosssectional area of the core and ΔP is the pressure drop across the corein Pa.

The interpolated curve from the simulation may be obtained by outputtingblock summary vectors for water saturation and k_(rw), and once thewater relative permeability curve used for the simulation is validatedagainst the experimental data, the apparent viscosity may be calculatedbased on Darcy's law.

The calculation of the interpolated k_(rw) may be based on the relativepermeability curves mentioned previously and on the capillarydesaturation function. The capillary desaturation function (an exampleof which is illustrated in FIG. 12) may be defined as follows (whereS_(or) is residual oil saturation):

$\begin{matrix}{F_{c\; d} = {1 - \frac{S_{or}\left( {{@{end}}\mspace{14mu} {of}\mspace{14mu} {flow}\mspace{14mu} {period}} \right)}{S_{or}\left( {{@{end}}\mspace{14mu} {of}\mspace{14mu} {initial}\mspace{14mu} {brine}\mspace{14mu} {flood}} \right)}}} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$

From there, the relative permeability may be calculated at the end ofeach flow period from:

k _(rw) _(interpolated) =F _(cd) k _(rw) _(straightline) +(1−F _(cd))*k_(rw) _(initial)   (Eq. 3)

and plotted against Sw=1−S_(or) (@end of flow period), an example ofwhich is illustrated in FIG. 13.

Next, the apparent viscosity may be calculated from Darcy's law:

$\begin{matrix}{\mu = \frac{{kk}_{{rw}_{interpolated}}A\; \Delta \; P}{QL}} & \left( {{Eq}.\mspace{14mu} 4} \right)\end{matrix}$

where k is the absolute permeability of the rock in m², k_(kw)_(interpolated) is the calculated interpolated relative permeability infraction, A is the cross sectional area of the core in m², ΔP is thepressure drop across the core in Pa, Q is the injection flow rate inm³/s and L is the length of the core in m. FIG. 14, for example,compares apparent viscosity calculations derived from multi-phasecorefloods with those derived from single-phase corefloods.

The aforementioned calculations may be validated by running a simulationof the EOR chemical coreflood experiment. As illustrated by FIGS. 15 and16, an excellent match for oil saturation in a core and pressure dropacross the core has been observed in one example embodiment.

FIG. 17, for example, illustrates an example sequence of operations 500for both determining an apparent viscosity for an aqueous polymercomposition used in a polymer flood and modeling a flow of the aqueouspolymer composition using the determined apparent viscosity consistentwith some embodiments of the invention. As shown in block 502, sequenceof operations 500 begins by generating a relative permeabilityinterpolation computer simulation model that is associated with acapillary desaturation function and that interpolates relativepermeability curves for a coreflood experiment. Next, in block 504, therelative permeability interpolation computer simulation model isvalidated, e.g., using experimental data generated from a corefloodexperiment using a water flood performed at a plurality of incrementalflow rates on a core plug, in the manner described above. In someembodiments, the validation of the model may include performing historymatching, and in some embodiments, the validation may include running acomputer simulation using the model in a reservoir simulator.

Next, in block 506, an interpolated relative permeability to water forthe aqueous polymer composition using experimental data generated fromthe coreflood experiment using a multi-phase flood with the aqueouspolymer composition, again in the manner described above. Then, in block508, the apparent viscosity of the aqueous polymer composition may bedetermined from the interpolated relative permeability to water in themanner described above. In some embodiments, as illustrated in block510, the determined apparent viscosity may also be validated, e.g.,using experimental data from the coreflood experiment.

It will be appreciated that the apparent viscosity of the aqueouspolymer composition will generally depend on the flow conditions, e.g.,the apparent shear rate, in the coreflood experiment. As such, in someembodiments, shear rate or another parameter related to flow conditions(e.g., flow velocity) may be calculated at different flow rates and theresult of the calculations may be used to determine apparent viscositybased on a table, graph or other data structure or representation thatmaps different values of apparent viscosity against apparent shear rate,flow velocity or another parameter related to flow conditions. In someembodiments, for example, the apparent viscosity may be plotted againstan apparent shear rate {dot over (γ)} calculated as follows:

$\begin{matrix}{\overset{.}{\gamma} = \frac{Q}{{A\left( {{Sw} - {Swcr}} \right)}\sqrt{k\; \phi}}} & \left( {{Eq}.\mspace{14mu} 5} \right)\end{matrix}$

where Q is the injection flow rate in m³/s, A is the cross sectionalarea of the core in m², (S_(w)−S_(wcr)) is the mobile water saturation,k is the absolute permeability of the rock in m² and φ is the porosity.

Next, as illustrated in block 512, the determined apparent viscosity,along with the relative permeability interpolation computer simulationmodel (as well as the capillary desaturation function embedded therein)may be used to model flow of the aqueous polymer composition, e.g., byrunning a simulation in a reservoir simulator. The simulation may beanother coreflood simulation for the purpose of modeling flow through acore, or may be a reservoir simulation for more modeling flow through areservoir, e.g., to simulate injection of the aqueous polymercomposition into a reservoir. It will be appreciated, however, that thedetermined apparent viscosity may be used in a number of otherapplications, e.g., to predict the injectivity of the injection wells,to determine the optimum injection rates and pressures for polymerinjection operations, etc.

Although the preceding description has been described herein withreference to particular means, materials, and embodiments, it is notintended to be limited to the particular disclosed herein. By way offurther example, embodiments may be utilized in conjunction with ahandheld system (i.e., a phone, wrist or forearm mounted computer,tablet, or other handheld device), portable system (i.e., a laptop orportable computing system), a fixed computing system (i.e., a desktop,server, cluster, or high performance computing system), or across anetwork (i.e., a cloud-based system). As such, embodiments extend to allfunctionally equivalent structures, methods, uses, program products, andcompositions as are within the scope of the appended claims.

While particular embodiments have been described, it is not intendedthat the invention be limited thereto, as it is intended that theinvention be as broad in scope as the art will allow and that thespecification be read likewise. It will therefore be appreciated bythose skilled in the art that yet other modifications could be madewithout deviating from its spirit and scope as claimed.

What is claimed is:
 1. A method of modeling a coreflood experiment, themethod comprising: generating a three dimensional computer simulationmodel of a core plug used in a coreflood experiment; and modeling in thethree dimensional computer simulation model of the core plug one or bothof a fluid introduction element or a fluid extraction element of a coreholder used in the coreflood experiment.
 2. The method of claim 1,wherein the core plug is homogeneous such that the three dimensionalcomputer simulation model has a plurality of grid cells having a sameproperty.
 3. The method of claim 1, wherein the core plug isheterogeneous such that the three dimensional computer simulation modelhas a plurality of grid cells with varying properties.
 4. The method ofclaim 1, further comprising running a simulation using the threedimensional computer simulation model in a computer-implementedreservoir simulator to model distribution and fingering of fluid flowproximate one or more faces of the core plug.
 5. The method of claim 4,wherein running the simulation includes modeling pressure drop acrossthe core plug.
 6. The method of claim 4, wherein thecomputer-implemented reservoir simulator comprises a general purposereservoir simulator, wherein generating the three dimensional computersimulation model is performed using a graphical pre/post-processor forthe general purpose reservoir simulation, and wherein the method furthercomprises displaying simulation results in three dimensions using thegraphical pre/post-processor.
 7. The method of claim 4, wherein the oneor both of the fluid introduction element or the fluid extractionelement modeled in the three dimensional computer simulation model anend effect in the coreflood experiment, and wherein running thesimulation includes modeling boundary conditions by representing thefluid introduction element as an injection well and representing thefluid extraction element as a production well.
 8. The method of claim 1,wherein modeling one or both of the fluid introduction element or thefluid extraction element includes modeling the fluid introductionelement and the fluid extraction element.
 9. The method of claim 1,wherein modeling the fluid introduction element and the fluid extractionelement includes modeling a plurality of ports in each of the fluidintroduction element and the fluid extraction element.
 10. The method ofclaim 9, wherein modeling the fluid introduction element and the fluidextraction element includes modeling a plurality of channels in each ofthe fluid introduction element and the fluid extraction element.
 11. Themethod of claim 10, wherein modeling the plurality of channels in eachof the fluid introduction element and the fluid extraction elementincludes modeling a plurality of circular channels.
 12. The method ofclaim 10, wherein modeling the plurality of channels in each of thefluid introduction element and the fluid extraction element includesmodeling a plurality of radial channels.
 13. The method of claim 1,wherein the three dimensional computer simulation model has a grid witha resolution that substantially matches that of a nuclear magneticresonance scanner used to determine oil saturation in the core duringthe coreflood experiment.
 14. The method of claim 1, wherein the one orboth of the fluid introduction element or the fluid extraction elementare symmetrical about one or more planes along an axis of symmetry ofthe core plug, and wherein generating the three dimensional computersimulation model and modeling one or both of the fluid introductionelement or the fluid extraction element includes modeling only a segmentof the core plug and the one or both of the fluid introduction elementor the fluid extraction element.
 15. The method of claim 14, wherein thefluid introduction element and the fluid extraction element are eachsymmetrical about a single plane, and wherein generating the threedimensional computer simulation model and modeling one or both of thefluid introduction element or the fluid extraction element includemodeling only a semi cylinder segment of the core plug and the one orboth of the fluid introduction element or the fluid extraction element.16. The method of claim 14, wherein the fluid introduction element andthe fluid extraction element are each symmetrical about a first andsecond orthogonal planes, and wherein generating the three dimensionalcomputer simulation model and modeling one or both of the fluidintroduction element or the fluid extraction element include modelingonly a quarter cylinder segment of the core plug and the one or both ofthe fluid introduction element or the fluid extraction element.
 17. Amethod of modeling fluid flow through a core plug in a corefloodexperiment, the method comprising: loading a three dimensional computersimulation model of a core plug that additionally models one or both ofa fluid introduction element or a fluid extraction element of a coreholder; and running a simulation using the three dimensional computersimulation model in a computer-implemented reservoir simulator to modelheterogeneous distribution of fluid flow proximate one or more faces ofthe core plug.
 18. The method of claim 17, wherein thecomputer-implemented reservoir simulator comprises a general purposereservoir simulator.
 19. The method of claim 18, wherein the one or bothof the fluid introduction element or the fluid extraction elementmodeled in the three dimensional computer simulation model an end effectin the coreflood experiment, and wherein running the simulation includesmodeling boundary conditions by representing the fluid introductionelement as an injection well and representing the fluid extractionelement as a production well.
 20. An apparatus, comprising: a memory,the memory storing a three dimensional computer simulation model of acore plug that additionally models one or both of a fluid introductionelement or a fluid extraction element of a core holder; at least oneprocessing unit; and program code configured upon execution by the atleast one processing unit to model fluid flow through a core plug in acoreflood experiment using the three dimensional computer simulationmodel.
 21. The apparatus of claim 20, further comprising program codeconfigured upon execution by the at least one processing unit togenerate the three dimensional computer simulation model and to model inthe three dimensional computer simulation model the one or both of thefluid introduction element or the fluid extraction element of the coreholder.
 22. A program product, comprising: a non-transitory computerreadable medium; and program code stored on the computer readable mediumand configured upon execution by at least one processing unit to modelfluid flow through a core plug in a coreflood experiment by running asimulation using a three dimensional computer simulation model of a coreplug that additionally models one or both of a fluid introductionelement or a fluid extraction element of a core holder, wherein runningthe simulation models a heterogeneous distribution of fluid flowproximate one or more faces of the core plug.